Polynomial Hulls of Sets Invariant Under an Action of the Special Unitary Group

Abstract

If K is a compact subset of Cn, will denote the polynomial hull of K: arises in the study of uniform algebras as the maximal ideal space of the algebra P(K) of uniform limits on K of polynomials (see [3]). The condition (K is polynomially convex) is a necessary one for uniform approximation on K of continuous functions by polynomials (P(K) = C(K)). If K is not polynomially convex, the question of existence of analytic structure in is of particular interest. For n = 1, is the union of K and the bounded components of C\K. The determination of in dimensions greater than one is a more difficult problem. Among the special classes of compact sets K whose polynomial hulls have been determined are those invariant under certain group actions on Cn.